The total angular defect is the sum of the Angular Defects
over all Vertices of a Polyhedron, where
the Angular Defect at a given Vertex
is the difference between the sum of face
angles and . For any convex Polyhedron, the Descartes total angular defect is

(1) |

(2) |

A Polyhedron with equivalent Vertices
is called a Platonic Solid
and can be assigned a Schläfli Symbol .
It then satisfies

(3) |

(4) |

(5) |

© 1996-9

1999-05-24